Express this quotient in scientific notation: ${\frac{2.800\times 10^{1}} {7.0\times 10^{-4}}}$
Explanation: Start by collecting like terms together. $= {\frac{2.800} {7.0}} \times{\frac{10^{1}} {10^{-4}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.40 \times 10^{1\,-\,-4}$ $= 0.40 \times 10^{5}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.40$ is the same as $4.00 \div 10$ , or $4.00 \times 10^{-1}$ $ = {4.00 \times 10^{-1}} \times 10^{5} $ $= 4.00\times 10^{4}$